Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page vii
... To find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 117 118 118 119 Area of the Surface of a Prism , Area of CONTENTS . vi.
... To find the Diameter of a Circle , 116 To find the length of an Arc , 117 Area of a Circle , Area of a Sector , Area of a Segment , Area of a Circular Ring , 117 118 118 119 Area of the Surface of a Prism , Area of CONTENTS . vi.
Page viii
... Prism , Area of the Surface of a Pyramid , PAGE . 120 120 Area of the Frustum of a Cone , Area of the Surface of a Sphere , 121 122 Area of a Zone , 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 ...
... Prism , Area of the Surface of a Pyramid , PAGE . 120 120 Area of the Frustum of a Cone , Area of the Surface of a Sphere , 121 122 Area of a Zone , 122 Area of a Spherical Polygon , 123 Volume of a Prism , 124 Volume of a Pyramid , 124 ...
Page 178
... prism ; lines in which the lateral faces meet , are called lateral edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis tance between the planes of its bases . 4. A RIGHT PRISM is one whose lateral edges are ...
... prism ; lines in which the lateral faces meet , are called lateral edges of the prism . 3. The ALTITUDE of a prism is the perpendicular dis tance between the planes of its bases . 4. A RIGHT PRISM is one whose lateral edges are ...
Page 179
... prism is one whose bases are quadrilaterals ; a pentangular prism is one whose bases are pentagons , and so on . 7. A PARALLELOPIPEDON is a prism whose bases are parallelograms . A Rectangular Parallelopipedon is a right ...
... prism is one whose bases are quadrilaterals ; a pentangular prism is one whose bases are pentagons , and so on . 7. A PARALLELOPIPEDON is a prism whose bases are parallelograms . A Rectangular Parallelopipedon is a right ...
Page 181
... prism is equal to the perim eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its conver surface equal to , ( AB + BC + CD + DE + EA ) × AF For , the convex surface is equal to the sum of all the ...
... prism is equal to the perim eter of either base multiplied by the altitude . Let ABCDE - K be a right prism : then is its conver surface equal to , ( AB + BC + CD + DE + EA ) × AF For , the convex surface is equal to the sum of all the ...
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence